%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC122+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:07:59 PM UTC 2026
% Result : Theorem 8.21s 1.90s
% Output : CNFRefutation 8.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 68 ( 24 unt; 0 def)
% Number of atoms : 259 ( 48 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 317 ( 126 ~; 115 |; 57 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 75 !; 20 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X3
& nil != X2 )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ~ rearsegP(X3,X2)
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X3
& nil != X2 )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( rearsegP(X3,X2)
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X3
| nil = X2 )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( rearsegP(X3,X2)
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X3
| nil = X2 )
& neq(X1,nil)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f243,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f244,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ? [X3] :
( app(X3,X1) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ rearsegP(X0,X1)
| ( app(sK12(X0,X1),X1) = X0
& ssList(sK12(X0,X1)) ) )
& ( ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) )
| rearsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f244]) ).
fof(f246,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( rearsegP(sK56,sK55)
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK56
| nil = sK55 )
& neq(sK54,nil)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f312,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| app(sK12(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f245]) ).
fof(f313,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ssList(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f245]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( rearsegP(sK56,sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f508,plain,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(definition_unfolding,[],[f502,f505,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f516,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f318]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ssList(sK12(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( app(sK12(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f507]) ).
tcf(c_248,negated_conjecture,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,negated_conjecture,
( rearsegP(sK56,sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_367,negated_conjecture,
rearsegP(sK56,sK55),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_371,negated_conjecture,
~ segmentP(sK56,sK55),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_249,c_248]) ).
tcf(c_8821,negated_conjecture,
~ segmentP(sK56,sK55),
inference(demodulation,[status(thm)],[c_371]) ).
tcf(c_8822,negated_conjecture,
rearsegP(sK56,sK55),
inference(demodulation,[status(thm)],[c_367]) ).
tcf(c_8823,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8824,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_12022,plain,
app(sK56,nil) = sK56,
inference(superposition,[status(thm)],[c_8824,c_232]) ).
tcf(c_17195,plain,
( ( app(sK12(sK56,sK55),sK55) = sK56 )
| ~ ssList(sK55)
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8822,c_66]) ).
tcf(c_17209,plain,
app(sK12(sK56,sK55),sK55) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_17195,c_8823,c_8824]) ).
tcf(c_25528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_26397,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_25528]) ).
tcf(c_26439,plain,
! [X0: $i] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(sK55)
| ~ ssList(X0)
| ~ ssList(sK12(sK56,sK55)) ),
inference(superposition,[status(thm)],[c_17209,c_26397]) ).
tcf(c_26483,plain,
! [X0: $i] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK12(sK56,sK55)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26439,c_8823]) ).
tcf(c_27560,plain,
( segmentP(sK56,sK55)
| ~ ssList(nil)
| ~ ssList(sK12(sK56,sK55)) ),
inference(superposition,[status(thm)],[c_12022,c_26483]) ).
tcf(c_27565,plain,
~ ssList(sK12(sK56,sK55)),
inference(forward_subsumption_resolution,[status(thm)],[c_27560,c_8821,c_141]) ).
tcf(c_27566,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| ~ rearsegP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_65,c_27565]) ).
tcf(c_27567,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27566,c_8823,c_8824,c_8822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC122+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.54 % Computer : n011.cluster.edu
% 0.11/0.54 % Model : x86_64 x86_64
% 0.11/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.54 % Memory : 8046.5625MB
% 0.11/0.54 % OS : Linux 6.8.0-71-generic
% 0.11/0.54 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Thu Sep 24 16:30:28 UTC 2026
% 0.11/0.55 % CPUTime :
% 0.11/0.55 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.60
% 0.14/0.60 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.60
% 0.14/0.60 % Detected problem language: tptp
% 0.14/0.61 % Proving...
% 8.21/1.90 % SZS status Started for theBenchmark.p
% 8.21/1.90 % SZS status Theorem for theBenchmark.p
% 8.21/1.90
% 8.21/1.90 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.21/1.90
% 8.21/1.90 % ------ iProver source info
% 8.21/1.90
% 8.21/1.90 % git: date: 2026-07-19 20:42:38 +0200
% 8.21/1.90 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.21/1.90 % git: non_committed_changes: false
% 8.21/1.90
% 8.21/1.90 % ------ Parsing...
% 8.21/1.90 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.21/1.90
% 8.21/1.90 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 8.21/1.90
% 8.21/1.90 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.21/1.90
% 8.21/1.90 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.21/1.90 % ------ Proving...
% 8.21/1.90 % ------ Problem Properties
% 8.21/1.90
% 8.21/1.90 %
% 8.21/1.90 % clauses 186
% 8.21/1.90 % conjectures 4
% 8.21/1.90 % EPR 55
% 8.21/1.90 % Horn 118
% 8.21/1.90 % unary 22
% 8.21/1.90 % binary 40
% 8.21/1.90 % lits 624
% 8.21/1.90 % lits eq 80
% 8.21/1.90 % fd_pure 0
% 8.21/1.90 % fd_pseudo 0
% 8.21/1.90 % fd_cond 21
% 8.21/1.90 % fd_pseudo_cond 14
% 8.21/1.90 % AC symbols 0
% 8.21/1.90
% 8.21/1.90 % ------ Schedule dynamic 5 is on
% 8.21/1.90
% 8.21/1.90 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.21/1.90
% 8.21/1.90
% 8.21/1.90 % ------
% 8.21/1.90 % Current options:
% 8.21/1.90 % ------
% 8.21/1.90
% 8.21/1.90
% 8.21/1.90 %
% 8.21/1.90
% 8.21/1.90 % ------ Proving...
% 8.21/1.90 %
% 8.21/1.90
% 8.21/1.90 % SZS status Theorem for theBenchmark.p
% 8.21/1.90
% 8.21/1.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.21/1.90
% 8.21/1.90
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